Conics And Cubics PDF Download
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Author | : Robert Bix |
Publisher | : Springer Science & Business Media |
Total Pages | : 300 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475729758 |
Download Conics and Cubics Book in PDF, ePub and Kindle
Algebraic curves are the graphs of polynomial equations in two vari 3 ables, such as y3 + 5xy2 = x + 2xy. By focusing on curves of degree at most 3-lines, conics, and cubics-this book aims to fill the gap between the familiar subject of analytic geometry and the general study of alge braic curves. This text is designed for a one-semester class that serves both as a a geometry course for mathematics majors in general and as a sequel to college geometry for teachers of secondary school mathe matics. The only prerequisite is first-year calculus. On the one hand, this book can serve as a text for an undergraduate geometry course for all mathematics majors. Algebraic geometry unites algebra, geometry, topology, and analysis, and it is one of the most exciting areas of modem mathematics. Unfortunately, the subject is not easily accessible, and most introductory courses require a prohibitive amount of mathematical machinery. We avoid this problem by focusing on curves of degree at most 3. This keeps the results tangible and the proofs natural. It lets us emphasize the power of two fundamental ideas, homogeneous coordinates and intersection multiplicities.
Author | : Robert Bix |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2008-11-01 |
Genre | : Mathematics |
ISBN | : 9780387511986 |
Download Conics and Cubics Book in PDF, ePub and Kindle
Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.
Author | : Henry Seely White |
Publisher | : |
Total Pages | : 16 |
Release | : 1906 |
Genre | : Curves, Cubic |
ISBN | : |
Download Triangles and Quadrilaterals Inscribed to a Cubic and Circumscribed to a Conic Book in PDF, ePub and Kindle
Author | : Séverine Fiedler - Le Touzé |
Publisher | : CRC Press |
Total Pages | : 238 |
Release | : 2018-12-07 |
Genre | : Mathematics |
ISBN | : 0429838247 |
Download Pencils of Cubics and Algebraic Curves in the Real Projective Plane Book in PDF, ePub and Kindle
Pencils of Cubics and Algebraic Curves in the Real Projective Plane thoroughly examines the combinatorial configurations of n generic points in RP2. Especially how it is the data describing the mutual position of each point with respect to lines and conics passing through others. The first section in this book answers questions such as, can one count the combinatorial configurations up to the action of the symmetric group? How are they pairwise connected via almost generic configurations? These questions are addressed using rational cubics and pencils of cubics for n = 6 and 7. The book’s second section deals with configurations of eight points in the convex position. Both the combinatorial configurations and combinatorial pencils are classified up to the action of the dihedral group D8. Finally, the third section contains plentiful applications and results around Hilbert’s sixteenth problem. The author meticulously wrote this book based upon years of research devoted to the topic. The book is particularly useful for researchers and graduate students interested in topology, algebraic geometry and combinatorics. Features: Examines how the shape of pencils depends on the corresponding configurations of points Includes topology of real algebraic curves Contains numerous applications and results around Hilbert’s sixteenth problem About the Author: Séverine Fiedler-le Touzé has published several papers on this topic and has been invited to present at many conferences. She holds a Ph.D. from University Rennes1 and was a post-doc at the Mathematical Sciences Research Institute in Berkeley, California.
Author | : Peter Rogers Sherman |
Publisher | : |
Total Pages | : 50 |
Release | : 1949 |
Genre | : Conic sections |
ISBN | : |
Download Nets of Conics and Their Associated Cubics Book in PDF, ePub and Kindle
Author | : Henry Seely White |
Publisher | : |
Total Pages | : 24 |
Release | : 1900 |
Genre | : Curves, Cubic |
ISBN | : |
Download Plane Cubics and Irrational Covariant Cubics Book in PDF, ePub and Kindle
Author | : Louis Antoine Victor De Cleene |
Publisher | : |
Total Pages | : 28 |
Release | : 1927 |
Genre | : Conic sections |
ISBN | : |
Download On Triangles Circumscribed about a Conic and Inscribed in a Cubic Curve Book in PDF, ePub and Kindle
Author | : Charles Clayton Grove |
Publisher | : |
Total Pages | : 60 |
Release | : 1907 |
Genre | : Collineation |
ISBN | : |
Download The Syzygetic Pencil of Cubics with a New Geometrical Development of Its Hesse Group, G216 Book in PDF, ePub and Kindle
Author | : Herman Walter Lautenbach |
Publisher | : |
Total Pages | : 188 |
Release | : 1940 |
Genre | : Mathematics |
ISBN | : |
Download Cramer's Paradox and Related Theorems Concerning Cubics and Conics Book in PDF, ePub and Kindle
Author | : Charles Herbert Clemens |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 2002-12-10 |
Genre | : Mathematics |
ISBN | : 0821833073 |
Download A Scrapbook of Complex Curve Theory Book in PDF, ePub and Kindle
This fine book by Herb Clemens quickly became a favorite of many algebraic geometers when it was first published in 1980. It has been popular with novices and experts ever since. It is written as a book of ``impressions'' of a journey through the theory of complex algebraic curves. Many topics of compelling beauty occur along the way. A cursory glance at the subjects visited reveals a wonderfully eclectic selection, from conics and cubics to theta functions, Jacobians, and questions of moduli. By the end of the book, the theme of theta functions becomes clear, culminating in the Schottky problem. The author's intent was to motivate further study and to stimulate mathematical activity. The attentive reader will learn much about complex algebraic curves and the tools used to study them. The book can be especially useful to anyone preparing a course on the topic of complex curves or anyone interested in supplementing his/her reading.